# Arithmetic Mean - DOC - DOC

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```					                                                                               Name: _____________ANSWERS IN BOLD______

1.   The collection of observations on the real world leading to the development of an abstract model is a process referred to as:
(a) deductive reasoning (b) inductive reasoning. (Circle the correct answer.)

2.   Five different ways of classifying data were identified. After each of the following write in its alternative:
Grouped                              UNGROUPED__________________________
Multivariate                         UNIVARIATE__________________________
Observational                        EXPERIMENTAL_______________________
Time Ordered                         CROSS SECTIONAL____________________
Continuous                           DISCRETE_____________________________
3.   Complete the following list of measurement scales in order of increasing sophistication of measurement:
NOMINAL_______________________
ORDINAL________________________
INTERVAL______________________
RATIO__________________________
4.   The following data were collected in a simple random sample of student heights in the population of all students enrolled in
last year's qsci-381 class: 62", 68", 74" and 76". What is the arithmetic mean height for this sample?
_____________70.00____________________

5.   Circle the icon (picture or button) on the toolbar that started the process to generate the chart shown here.

SEE BOLD ARROW ON CHART
6.   Indicate the best match-up of the following summary statistics with both a key advantage and disadvantage. One advantage and
one disadvantage should be indicated for each of the three statistics (No duplications).

Arithmetic Mean:      _A_       Applicable even to nominal data:          __C_   Time Consuming when done by hand:       __B_

Median:               _B_       A weighted average is possible:           __A_   Easily distorted by extreme values:     __A_

Mode:                 _C_       Not easily distorted by extreme values:   __B_   May not be unique:                      __C_

7.       When a distribution has a positive skew it is typically found that (select one by circling):
Mean = Median = Mode
Mean < Median < Mode
Mean > Median > Mode

8.       Consider the following screen window:

a.        In order to generate the boxed information labeled "Column 1" two more items in the Descriptive Statistics window
had to be left clicked. Circle those two items.
b.        Under which of the pull-down labels at the top of the screen window is the Descriptive Statistics window to be
found. Circle the label.
c.        The IQR is not shown in the boxed information and it can thereby be concluded that we have insufficient data (15
observations) for its calculation (circle one).       TRUE              FALSE

9.       A simple random sample of student heights consisted of the observations: 62", 68", 74" and 76". The sample mean height

was calculated to be 70". What is the standard deviation for this sample?               ___________6.3"___________

In answering the questions of this quiz refer to the Venn diagram shown below.
HHH                            TTH

HHT                            THT

HTH                            HTT

THH                            TTT

A fair coin is flipped three times and the results recorded as either heads (H) or tails (T) in the order in which they appear. All possible
outcomes of this experiment are shown in the Venn diagram. The number of heads (or tails) observed when this experiment is
conducted will be indicated in the questions that follow. For example, H=2 is observed to occur in 3 of the outcomes. Another
example would be that T>1 is observed in 4 outcomes. A final example is that [(H2)(T1)] is observed in 3 outcomes.

10.      If each outcome has equal probability of being observed calculate the following probabilities (fractions acceptable).

a.   P{H=3} =                                      ________1/8____________

b.   P{T<2} =                                      ________4/8____________

c.   P{1T2} =                                    ________6/8____________

d.   P{(H1)(T1)} =                              ________6/8____________

e.   P{(H2)(T3)} =                              ________5/8____________

f.   P{H=2T1} =                                  ________3/4____________

g.   P{H2} + P{T2} =                             _________1____________

h.   This last result (g.) is due to the two events being (circle one):    EXHAUSTIVE        MUTUALLY EXCLUSIVE          BOTH

i.   Are the events (H2) and (1T2) statistically independent? (circle one)       YES      NO        CANNOT BE DETERMINED

11.      Accurately complete the bar chart shown below.

PROBABILITY DISTRIBUTION
PRO BABILITY

H=0         H=1        H=2      H=3

12.      In a survey of family dwellings in a Seattle neighborhood the total number of adults plus children living in each house on
July 1 of last year was recorded. These data are: (Circle one item in each of the following five columns.)
1                2                     3                           4                 5
cross-sectional    univariate            observational             discrete           grouped
time ordered       multivariate          experimental              continuous         ungrouped

13.   Match the listed data descriptions with their measurement scale.
Nominal..(N)                              Military Rank Listed on Person's Service Record                 ____O___
Ordinal...(O)                             Body Temperature in Degrees Centigrade                          ____I___
Interval...(I)                            Weight of an Individual in pounds                               ____R___
Ratio.....(R)                             Self-declared Ethnic group of an individual                     ____N___
14.   The following four sample observations have been drawn from a normal distribution: 50, 50, 70 and 80. (Give numerical
answers to two decimal places for all questions.)
Calculate the following statistics:
a.        The mean is:                                            ___62.50______
b.        The standard deviation is:                              ___15.00______
c.        The standard error of the mean is:                      ____7.50______
15.   In responding to the following questions refer to the Venn diagram shown here. There are ten outcomes, each of which is
indicated with an asterisk, and each of which has equal probability of occurring. There are three events, each of which is
indicated by a circle circumscribing its associated outcomes.

*
*
A                                     *
*            *
C
*
*
*         *                               *

B                               S

1.       P{B} =                      ___.60______
2.       P{AB} =                    ___.30______
3.       P{BC} =                    ___.80______
4.       P{CB} =                    ___.33______
16.   The arithmetic mean number of adults plus children living in single-family housing units in the United States on July 1 of last
year is defined to be the population parameter of interest in a demographic study. Not all of the dwellings can be surveyed so
that a sample of 1000 is randomly selected. From previous work it thought very likely that the population is bimodal and that
it has a strong positive skew. The variate, number of adults plus children, is discrete. A point estimate and a confidence
interval for the population parameter are needed. Your colleague argues that while the sample mean is a suitable point
estimate it is impossible to establish a confidence interval because of the peculiar nature of the population distribution.
Do you agree with him based on what we have studied so far this quarter?                                YES               NO

17.   Using the attached tables answer the following questions (numerical answers to 3 decimal places):
A normally distributed random variable has a population mean of 50 and a population standard deviation of 10. One
observation will be drawn from this population.
a.        What is the probability that the value of this observation will exceed 60?
____0.159___
b.        What is the probability that it will fall between 35 and 55?
____0.625___
Midterm Example A

I.     Circle the best answer for the following questions:
A.       For any symmetric distribution the arithmetic mean, mode and median all coincide.              TRUE               FALSE
B.       The concept of the median can only be applied to interval and ratio data.                      TRUE               FALSE
C.       Ambient temperature can be measured using any of the four scales discussed.                    TRUE               FALSE
D.       The concept of the standard deviation can only be applied to interval and ratio data.          TRUE               FALSE
E.       The histogram is an unambiguous way of finding the mode for ratio data.                        TRUE               FALSE
II.    A simple random sample consists of the following three observations (ratio data): 68, 100, and 54. Circle the answer for:
A.       the arithmetic sample mean?                              74       68        71.2     Cannot be calculated or not given
B.       the sample variance?                                     23.6     19.4      556.0    Cannot be calculated or not given
C.       the population median?                                   100      77        68       Cannot be calculated or not given
D.       the sample range?                                        14       46        100      Cannot be calculated or not given
E.       Q2 of the sample                                         68       61        84       Cannot be calculated or not given
III.   Answer the questions that follow by referring to the Venn diagram given below. The outcomes, each with equal probability
of occurring are generated by randomly drawing one card from the following eight: 2, 4 and 6 of hearts, 4 of clubs, 4 and 8
of spades, and, the 2 and 8 of diamonds (the notation in the diagram is self-explanatory).

H2      H4       H6
C4
S4                S8
D2                        D8
Note that P{4} = 3/8, P{S} = 2/8, etc.
A.       P{HD} = ?                            _______________________
B.       P{H4} = ?                            _______________________
C.       P{CS48} = ?                        _______________________
D.       Is the probability of drawing a heart statistically independent of that of drawing a four?              YES       NO
E.       Is the probability of drawing a spade statistically independent of that of drawing a four?              YES       NO
IV.    A single fair die, with the usual six sides numbered 1, 2, 3, 4, 5 and 6, will be rolled and the number on the showing face
noted. If a 1 or 6 is observed then the roll will be termed a "success" otherwise it is a "failure". This die will be rolled 18
times and the number of successes recorded.
A.        The probability of "success" is:                                                               _________________
B.       The mean of this distribution is:                                                              _________________
C.       The standard deviation of this distribution is:                                                _________________
D.       The probability of exactly 4 successes is (write out the formula with numbers entered):        _________________
E.       This distribution is skewed to the:                                                            _________________
V.     From previous plant survey studies it has been found that a particularly rare plant species is randomly distributed over an
extensive area with a mean number of individuals per square mile of 2. The application of the Poisson distribution has been
found to be appropriate for statistical calculations in this case. (Where formulas are called for in the following questions
substitute numbers so that it is ready to be solved on a calculator.)
A.        The variance of this distribution is:                                                         _________________
B.       The mean number of individuals per township (36 mi2) is:                                       _________________
C.       The probability of less than 2 individuals within one square mile is (formula):                _________________
D.       This distribution is skewed to the:                                                             _________________
E.       The probability of 1 or more individuals within one square mile is (formula):                   _________________
VI.   A continuous uniform distribution runs from 0 to 10 and is sketched below. Note that the shaded region has an area of 1.0 as
would be expected. The mean of the distribution is 5 and 2.89 is its standard deviation. Answer the questions that follow with
regard to this particular distribution.

1/10

0                         10
A.       The median of this distribution is:                                                             _________________
B.       The probability that one randomly selected number from this distribution would have a value between 4 and 6 is:
_________________
C.       A random sample of 36 observations will taken from this distribution and a sample mean will be calculated. The
probability that the sample mean will fall between 4 and 6 is:                                  _________________
D.       There is a 40% chance that the sample mean will be less than:                                   _________________
E.       These last two solution procedures were based on what theorem?                                  _________________

VI.   Respond to the questions that follow by referring to the Excel screen view shown here:

A.       Complete the formula that is being typed:                                  ___________________________
B.       Circle the pull-down menu item that was left-clicked to generate the "Descriptive Statistics" results (shaded area).
C.       Put an arrow to the icon that will, with one left-click followed by enter, place the sum of all rainfall depths in cell
B18.
D.       Circle the icon that eventually leads to the function that generates the content of cell F17.
E.       Put an arrow to the pull-down menu item that leads a data sorting operation.
Midterm Example B

I.(8)    The following three observations on male student heights have been selected at random from the entire population of enrolled
male students at the University of Washington:       67, 74 and 69.

A.       What is the value of the arithmetic mean for this sample?                           __________________

B.       What is the value of the standard deviation for this sample?                        __________________

II.(8)   A sample of 36 observations has been taken from a population that is known to have a population variance of 324 and a
population mean of 18.

A.       What is the probability that the sample mean will have a value greater than 21? __________________

B.       What is the probability that the sample mean will fall between 12 and 24?           __________________

III.(12) There are 50 people enrolled in a class; 30 of them are women and 20 are men. Of the women 20 have brown eyes and 10
have some other eye color. The men are evenly divided; half have brown eyes and half have eyes of another color. One
person will be drawn at random from this group of 50. Give the probability of the following events:

A.       A man is drawn:                                                                     __________________

B.       A person with brown eyes is drawn:                                                  __________________

C.       A man is drawn given that the person has brown eyes:                                __________________

D.       A brown eyed person is drawn given that the person is a woman:                      __________________

IV.(16) A biased coin will be flipped and the number of times that heads appears out of 20 flips will be counted. There is a
probability of 0.60 that heads will show on any given flip of the coin. Answer the following questions with respect to this
experiment. (Substitution of numbers into the appropriate formula is sufficient - no need to reduce.)

A.       What is the expected number of heads that will be observed in this experiment? __________________

B.       What is the variance of this distribution?                                          __________________

C.       What is the probability of observing exactly 10 heads in this experiment?           __________________

D.       This distribution is (circle one):                positively skewed       skewed left      symmetric

V.(8)    Indicate whether the following are true or false with respect to the Poisson distribution:

A.       The random variable can take on any integer value from zero to infinity                    True    False

B.       The mean of the distribution is the same as its variance                                   True    False

VI.(16) A random variable follows a continuous uniform distribution and can take on values from 50 to 100. Answer the following
questions with regard to this distribution:

A.       The mean of this distribution is:                                                   __________________

B.       The standard deviation of this distribution is:                                     __________________

C.       The probability of observing a value less than 60 for the random variable is:       __________________

D.       A sample mean based on 100 observations from this distribution follows the normal distribution with:

1.       A mean of:                                                                 __________________

2.        A standard error of the mean of:                                     __________________
VII.(16) Consider the following Excel screen where 20 observations are being numerically analyzed:
A.       Provide the necessary information for the appropriate boxes in the "Descriptive Statistics" window if the mean and
standard error of the mean are to be calculated using this tool.

B.       The data shown in cells E12:E16 was generated using the "frequency" function. The last step in the process of

invoking and executing this function involves pressing what key(s)?              __________________

C.       The total shown in cell B23 was found by right-clicking on a toolbar icon and then pressing the enter key on the
keyboard. Circle the icon.

D.       These 20 observations could be sorted using Excel. Where do you find the sorting operation? Indicate its location on
the screen with an arrow.

VIII.(16) A simple random sample of 36 observations is to be taken from a population with the following parameters:  = 200 and 2 =
100.

A.       There is a 95% chance that the sample mean will fall between ___________ and ___________.

B.       There is a 60% chance that the sample mean will be less than ___________.

C.       These results are obtainable because of the Central Limit Theorem.               True              False

D.       A Q-Q plot of these 36 observations must show something close to a straight line in order to use the normal table for

the calculations of parts A and B above.                                True              False
Midterm Example C

I.(15)    The following table lists the outcomes and associated probabilities assignable to a "loaded" die. Complete the following table

x                       P{X=x}                             xP{X=x}                     (x-)2P{X=x}
1                         0.1
2                         0.2
3                         0.2
4                         0.2
5                         0.1
6                         0.2

A.       The expected value of the random variable X is:                             _________________________

B.       The variance of the random variable X is:                                   _________________________

C.       This is an example of a ( discrete      continuous ) random variable (circle one).

II.(20) The loaded die of the previous question will be rolled 5 times. If the die shows a 5 or a 6 the roll will be termed a "success",
otherwise the roll is deemed a "failure".

A.       The probability of "success" on any given roll of the die is:               _________________________

B.       The expected number of "successes" in 5 rolls of the die is:                _________________________

C.       The probability of observing exactly 1 success in the five rolls is:        _________________________

D.       The name of this distribution is the:                                       _________________________

III.(6)   A pair of dice are rolled 30 times, the sums recorded, and the following values calculated from these numerical observations:
the mean is 5.833 and the standard deviation is 1.877

A.       These two values are (parameters        statistics) of the distribution (circle one).

B.       It is known that the sample mean follows the normal distribution because of the ______________theorem.

IV.(25) When rolled a pair of fair dice have an expected value of 7 and a variance of 5.8333 for the sum of the showing faces; denote
this sum by X. The dice will be rolled 36 times and the sample mean calculated; denote the sample mean by X . Complete
the following:

A.       P{ X  7} = ?

B.       P{ X  8} = ?

C.       P{ X  6} = ?

D.       P{6.5  X  7.5} = ?

E.       P{ X  ?} = 0.65

V.(6)     The proportion of students who are engineering majors at the University is 15%. If 100 students are chosen at random from
the student body answer the following questions with regard to the sample proportion, p, observed.

A.       P{p  0.20} = ?

B.       P{p  ?} = 0.40
VI.(20) There are 10 possible outcomes for an experiment, all of equal probability. Some of these outcomes belong to one or more of
three events: A, B and C. The Venn diagram below shows these events with their associated outcomes (asterisks). Answer the
questions that follow by referring to the diagram.

*                        B
*       * *             *
*
*                          *
* A   *                    C
S

A.       P{A} = ?

B.       P{A  B} = ?

C.       P{A  B} = ?

D.       Events C and B are statistically independent ( True        False ).

VII.(8) Answer the following questions with regard to the Excel screen shown below.

A.       Complete the equation that is being typed. _________________________________

B.       The Quartile function is found by first left-clicking on what toolbar item. (circle it.)

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 views: 10 posted: 12/14/2011 language: pages: 10